What is the surface area of this cylinder? The radius is 8.1 ft and the height is 13.6 ft Surface area = Atop + Abottom + Aside Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. Find the radius and height of the cylinder. The circle on the bottom of the cylinder is the same, so: Find the circumference of the top circle. Now find the area of the curved surface. The curved surface is a rectangle. One side length is the height, and the other side length is the circumference of the circle. Now add the areas to find the surface area of the cylinder. The surface area of the cylinder is about _____ square feet

Answer 1

To calculate the surface area of the cylinder, we need to find three components: the area of the top circle, the area of the bottom circle, and the lateral (curved) surface area.

1. Given dimensions:

   • Radius \( r = 8.1 \) ft
   • Height \( h = 13.6 \) ft

2. Area of the top circle (A_top): \[ A_{top} = \pi r^2 = 3.14 \times (8.1)^2 \] \[ A_{top} = 3.14 \times 65.61 \approx 206.57 \text{ square feet} \]

3. Area of the bottom circle (A_bottom): Since the bottom circle is the same as the top circle, we have: \[ A_{bottom} = A_{top} \approx 206.57 \text{ square feet} \]

4. Circumference of the top circle (C): \[ C = 2 \pi r = 2 \times 3.14 \times 8.1 \] \[ C = 6.28 \times 8.1 \approx 50.8 \text{ feet} \]

5. Area of the curved surface (A_side): The area of the curved surface can be thought of as a rectangle where the height is \( h \) and the width is the circumference \( C \): \[ A_{side} = C \times h = 50.8 \times 13.6 \] \[ A_{side} \approx 691.68 \text{ square feet} \]

6. Total surface area (A_total): \[ A_{total} = A_{top} + A_{bottom} + A_{side} \] \[ A_{total} \approx 206.57 + 206.57 + 691.68 \] \[ A_{total} \approx 1104.82 \text{ square feet} \]

Finally, rounding to the nearest hundredth, the surface area of the cylinder is approximately 1104.82 square feet.